1. Field of Invention
This invention relates to methods of transforming data from the time domain to the frequency domain and to spectrographic devices, which convert time-domain information, such as audio signals, into a frequency-domain representation of this information.
2. Description of Prior Art
Methods of transforming time domain data to the frequency-domain using the methods of Fourier have been used for many years. Prior to the development of the Fast Fourier Transform technique (FFT) in the 1960s, Fourier transformation was extremely expensive computationally and was thus rarely used. The development of the FFT has made Fourier analysis much more efficient and practical and it has since found more widespread use. However, the FFT is still a computationally expensive technique, which has limited the performance of devices, such as digital spectrographs, which utilize it.
Spectrographs have been available for many years. Originally implemented as strictly analog devices, early spectrographs recorded spectrograms on a spinning drum, using an electric arc and special paper. These devices were severely limited in their ability to process and analyze input signals. They also were of limited resolution and their output was not useable in realtime since the drum had to be stopped and the paper unloaded. These devices also had a limited operating time, since the paper was quickly filled with spectrographic output.
Another frequency-domain device, the spectrum analyzer, is essentially a receiver which is swept through a range of frequencies, displaying the amplitude of received signals on a cathode ray tube. The use of one receiver to sequentially detect many different frequencies results in each frequency being detected only intermittently, with relatively long periods during which no detection occurs for each given frequency. Such an instrument is of limited usefulness in analyzing dynamic signals, i.e. signals in which the frequency spectra is changing and in which signals may be present at specific frequencies for a short time only.
To address these limitations, in recent years realtime spectrographs have been implemented on digital computers. The conversion of time domain to frequency domain is typically done in digital systems by using the mathematical method known as the Fast Fourier Transform (FFT). The Transform is computationally expensive and thus the conversion is typically performed by either a powerful mainframe computer or by a dedicated auxiliary processing unit known as a Digital Signal Processor (DSP). The hardware required by these systems is expensive and thus the systems themselves are generally found in a relatively small number of research laboratories. Many potential applications of realtime spectrographs are not currently realized due to the high cost of the hardware required.
Until now it has been generally assumed that the computational complexity of time-domain to frequency-domain transformation precluded the accomplishment of such transformation in realtime at any useful level of resolution on a microprocessor unassisted by a DSP. Indeed the DSP/Acquisition Board Selection Guide published by Hyperception, Inc. states flatly "If you intend to do ANYTHING to the data as it is going in or coming out in real-time, you must have a DSP. You will not be able to write optimized code to do some "simple processing" like vector transformations or adding offsets."
A search of the prior art represented in issued U.S. patents reveals a number of devices of interest to this application.
U.S. Pat. No. 4,641,343 to Holland et al. shows a microprocessor-based real time speech formant analyzer and display. This device detects voice formants F0, F1 and F2 and indicates the strength of formants F1 and F2 by moving an indicator through the x and y dimensions of a video display. Such a display enables a deaf user to identify vowels by the indicator's position on the screen, but it does not present a spectrograph. The strengths of only two frequencies, F1 and F2, are displayed and not the full range of frequencies used in speech communications. F1 and F2 are typically below about 1000 Hz. Many important features of vocal productions, and especially of fricatives, lie above this frequency in the range 1 kHz to 8 kHz.
Similarly, U.S. Pat. Nos. 4,276,445 and 4,401,805 to Harbeson demonstrate devices which display in realtime the strength of only the fundamental pitch, F0. U.S. Pat. No. 4,833,716 to Cote, Jr., shows a device which displays the relative power of only four frequency bands.
All prior methods of generating spectrographic displays suffer from one or more of the following disadvantages:
(a) They are not truly realtime devices, requiring that paper traces be loaded and unloaded, for example.
(b) They offer only intermittent representation of dynamic signals, as with spectrum analyzers.
(c) They do not offer continuous, uninterrupted realtime spectrographic display.
(d) They require the use of expensive data processing hardware such as mainframe computers or dedicated Digital Signal Processors.
(e) They provide realtime analysis of only one, or at most a small number, of frequencies.
(f) They offer relatively limited resolution of rapidly changing, dynamic signals.
(g) They display spectral power in a manner which makes accurate interpretation of spectral power difficult.
(h) They utilize a linear frequency axis which results in wasteful use of display area, which limits the total length of input signal which may be represented on a single display. In addition, the linear frequency axis makes visual interpretation of results relatively difficult.
As will be shown, the realtime embodiment of the present invention suffers none of these limitations.